Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

Zhang, Yuanzhao; Lucas, Maxime; Battiston, Federico

doi:10.48550/arxiv.2203.03060

Cited by 3 publications

(3 citation statements)

References 39 publications

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“…So far, we have seen that graphs constitute adequate models for representing complex interactions in chemical mixtures. However, the GNN representation is limited to pairwise interactions, suggesting the use of hypergraphs to capture richer structural information . Incorporating temporal dynamics into GNNs is possible through the Koopman operator .…”

Section: Ann For Nanoscale Mixturesmentioning

confidence: 99%

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the ’recomposition’ of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure–Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

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Section: Ann For Nanoscale Mixturesmentioning

confidence: 99%

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Nicolle,

Deng,

Ihme

et al. 2024

J. Chem. Inf. Model.

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“…Such higher-order interactions have been observed in a wide variety of systems, including collaboration networks (6), cellular networks (7), drug recombination (8), human (9) and animal (10) face-to-face interactions, and structural and functional mapping of the human brain (11)(12)(13). Moreover, the higher-order organization of many interacting systems is associated with the generation of new phenomena and collective behavior across many different dynamical processes, such as diffusion (14,15), synchronization (16)(17)(18)(19)(20)(21), spreading (22)(23)(24) and evolutionary games (25,26).…”

Section: Introductionmentioning

confidence: 99%

Generalized Inference of Mesoscale Structures in Higher-order Networks

Ruggeri¹,

Contisciani²,

Battiston³

et al. 2023

Preprint

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Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of higher-order data. Our approach recovers community structure with accuracy exceeding that of currently available state-of-the-art algorithms, as tested in synthetic benchmarks with both hard and overlapping ground-truth partitions. Our model is flexible and does not impose restrictive assumptions encountered in previous works, allowing to capture unexplored mesoscale configurations, such as disassortative community structure. Moreover, our method scales orders of magnitude faster than competing algorithms, making it suitable for the analysis of very large hypergraphs, containing millions of nodes and interactions among thousands of nodes. Our work constitutes a practical and general tool for hypergraph analysis, broadening our understanding of the organization of real-world higher-order systems.

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“…Researchers have recently expanded the study of synchronization to the framework including higherorder network structures, with the majority of them opting for simplicial complexes to simulate group interactions due to their simple topological representation [33,34]. The presence of many-body interactions has been linked to the emergence of abrupt synchronization transitions [28,[35][36][37], improvement of synchronization [38,39], multistability [40], cluster synchronization [41], antiphase synchronization [42], chimeras [43], etc. These findings have coincided with the development of analytical paradigms for interpreting coupled oscillators with many-body interactions, such as Hodge decomposition [44,45], Laplacian operators [46,47], and low dimensional descriptions [48].…”

Section: Introductionmentioning

confidence: 99%

Stability of synchronization in simplicial complexes with multiple interaction layers

Anwar

Ghosh

2022

Phys. Rev. E

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Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic Rössler oscillators and Sherman neuronal models, and demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.

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Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes

Cited by 3 publications

References 39 publications

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Generalized Inference of Mesoscale Structures in Higher-order Networks

Stability of synchronization in simplicial complexes with multiple interaction layers

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